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Chinese Physics Letters

Bose—Einstein Condensation in a Spherical Symmetric Harmonic Trap

颜家玉, 卢竞

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

Using a perturbation theory approach,we derive an approximate analytical solution of the Gross-Pitaevskii equation in a spherical symmetric harmonic trap.This solution is consistent with that obtained numerically.

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An approximate solution to the Gross-Pitaevskii equation for Bose-Einstein condensate in a spherical harmonic trap is suggested, which is valid in the whole interval of the coupling parameter, correctly interpolating between weak-coupling and strong-coupling limits. This solution is shown to be more accurate than the optimized Gaussian approximation as well as the Thomas-Fermi approximation. The derivation of the solution is based on the self-similar approximation theory. The possibility of obtaining interpolation formulas in the case of nonspherical traps is discussed.
Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrödinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.